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Torus

For major radius $R$ and minor radius $r$ with $R>r>0$, the standard embedded torus of revolution in $\mathbb R^3$ is
$$
(\sqrt{x^2+y^2}-R)^2+z^2=r^2.
$$
It is parametrized by
$$
(s,t)\longmapsto
\bigl((R+r\cos 2\pi t)\cos2\pi s,
(R+r\cos2\pi t)\sin2\pi s,
r\sin2\pi t\bigr),
$$
which identifies the opposite sides of the unit square.


Embedded torus of revolution

Past exam of the mathematics course of the University of Cambridge / 2005 / ib / Paper 1 / 2A / Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 4 / 13G / c / Solution

Embedded torus of revolution

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Embedded torus of revolution

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